Abstract: Branching structures are based on geometric systems that expand through bifurcation without returning to form closed cells. In this sense, branching structures resemble the structure of trees that branch continually outward. In architectural engineering, these forms can be used either as tension or compression systems. Numerous built examples have been produced since the initial inspiring studies made by Frei Otto in the early 1960's. Form finding techniques based on models have been used in the past to study these forms. Although thread models can be effective in the study of force paths, they cannot distinguish between tension and compression and have no way to take member buckling into account. But buckling does have an influence on appropriate geometry of a compression system. Also, minimal paths (or pseudo minimal paths based on surface tension thread models) have been used to explore possible geometries for branching structures. In this paper, both surface tension thread models dipped in water, and weighted string models are shown in comparison with ideal tension and compression forms found with a computational method based on Genetic Algorithms. The same computational model is used to find geometries with minimal overall member length. Both 2D and 3D geometries are derived.